By John H. Miller and Scott E. Page
Princeton University Press (March 5, 2007)
Miller and Page's book provides an introduction into the computational, agent based, modeling of complex adaptive systems, and gives the reader what I hope to be an overview about the present day status of ideas and concepts. It's a bit hard to tell for me, since it's the first book I read on the topic.
They motivate the possible importance of these studies for the understanding of social, political, and economical dynamics. Though the motivation is plenty, the book lacks some convincing examples where this modeling has actually proved to be useful. Maybe there just are none? I am left with a feeling of an area that has a vast potential, but whose actual relevance is presently more or less unclear.
The main theme of the book is the 'Interest in Between'. In between not only in between computational modeling an social life, but also in between very few and infinitely many agents, in between equilibrium and chaos, in between omniscient and utterly stupid agents, in between uniformity and individualism (call it homogeneity and heterogeneity) - cases in which mathematical proof of a system's behavior is only rarely possible, and numerical simulations become increasingly important.
The book is well structured, and after some examples to catch the reader's interest, it starts with a general discussion about how reducing the study of a system to a study of its constituents does not shed light on emerging features. They continue with a chapter on what makes a good model. A chapter that I find unnecessarily defensive, but it seems to be aimed at a different audience than theoretical physicists.
In the following chapters the examples become gradually more sophisticated, and illuminate the importance of various ingredients to the modeling, such as the order of updating, the intelligence of the agents, or communication between them, and selection rules that allow the complex system to 'adapt', and the relevance of living on 'the edge of chaos'. In several places, the authors provide a mathematical proof for features of certain models that they discuss. I admit on not actually following these proofs since I don't presently need them, but it's useful to know they are there.
However, in several subsections the discussion gets lost into details that the reader can't follow merely from what was explained earlier, and it requires more knowledge than what the authors provide. As an example, in Section 10.3.2 I learned
"The four games with the highest variations consisted of all the games with a single, iterated dominant strategy equilibrium that was Pareto dominated by a non-Nash outcome. Besides the Prisoner's Dilemma, two other symmetric games had above-average measures of outcome variation: Chicken, which was fifth, and Battle of the Sexes which was sixteenth."
I am either a very sloppy reader or besides the Prisoner's Dilemma indeed none of the other games was previously explained. Neither do I have any clue what Pareto dominated means or what a non-Nash outcome is. One can surely look this up elsewhere, but sections like this leave me with the impression of a reprint of a paper (which might actually be the case, I haven't yet checked the reference list.) Also, in various places, figures appear that are reprints from other publications, but what is actually shown on the figure is not well explained. E.g. the variables in figure 12.1 just remain undefined. Though this isn't of much relevance to the context, the only purpose for such figures seem to be to just have a figure.
As to the writing style, it is very mixed, and ranks from almost poetic paragraphs with a subtle sense of humor to alignments of very dry and technical explanations. It makes me wonder whether the writing was shared between the authors, or as speculated above, was filled up with pasting in extracts from papers in scientific journals. In several places the general motivation is somewhat repetitive.
Also, it is mentioned somewhere in the book that even though there is no exact definition for complexity, there are definitions that are useful in certain cases. Given that this is one of the main themes in the book, I would have liked to hear more about this.
The book has two appendices, the first is essentially an outlook with various open questions, which I find very interesting. The second one are 'practices for modeling' which are advices for how to write a good numerical code.
Taken together, it is a good book, but depending on your knowledge it either contains too much or too little information. It is however a useful book to have because it's the first of this kind. If this was an amazon review, I'd give three stars.